Efficient generation of feasible pathways for protein conformational transitions

We develop a computationally efficient method to simulate the transition of a protein between two conformations. Our method is based on a coarse-grained elastic network model in which distances between spatially proximal amino acids are interpolated between the values specified by the two end conformations. The computational speed of this method depends strongly on the choice of cutoff distance used to define interactions as measured by the density of entries of the constant linking/contact matrix. To circumvent this problem we introduce the concept of using a cutoff based on a maximum number of nearest neighbors. This generates linking matrices that are both sparse and uniform, hence allowing for efficient computations that are independent of the arbitrariness of cutoff distance choices. Simulation results demonstrate that the method developed here reliably generates feasible intermediate conformations, because our method observes steric constraints and produces monotonic changes in virtual bond and torsion angles. Applications are readily made to large proteins, and we demonstrate our method on lactate dehydrogenase, citrate synthase, and lactoferrin. We also illustrate how this framework can be used to complement experimental techniques that partially observe protein motions.     

Phylogenetic utility of the nuclear gene arginine decarboxylase: an example from Brassicaceae

Arginine decarboxylase (ADC) is an important enzyme in the production of putrescine and polyamines in plants. It is encoded by a single or low-copy nuclear gene that lacks introns in sequences studied to date. The rate of Adc amino acid sequence evolution is similar to that of ndhF for the angiosperm family studied. Highly conserved regions provide several target sites for PCR priming and sequencing and aid in nucleotide and amino acid sequence alignment across a range of taxonomic levels, while a variable region provides an increased number of potentially informative characters relative to ndhF for the taxa surveyed. The utility of the Adc gene in plant molecular systematic studies is demonstrated by analysis of its partial nucleotide sequences obtained from 13 representatives of Brassicaceae and 3 outgroup taxa, 2 from the mustard oil clade (order Capparales) and 1 from the related order Malvales. Two copies of the Adc gene, Adc1 and Adc2, are found in all members of the Brassicaceae studied to data except the basal genus Aethionema. The resulting Adc gene tree provides robust phylogenetic data regarding relationships within the complex mustard family, as well as independent support for proposed tribal realignments based on other molecular data sets such as those from chloroplast DNA.      

vGNM: a better model for understanding the dynamics of proteins in crystals

The dynamics of proteins are important for understanding their functions. In recent years, the simple coarse-grained Gaussian Network Model (GNM) has been fairly successful in interpreting crystallographic B-factors. However, the model clearly ignores the contribution of the rigid body motions and the effect of crystal packing. The model cannot explain the fact that the same protein may have significantly different B-factors under different crystal packing conditions. In this work, we propose a new GNM, called vGNM, which takes into account both the contribution of the rigid body motions and the effect of crystal packing, by allowing the amplitude of the internal modes to be variables. It hypothesizes that the effect of crystal packing should cause some modes to be amplified and others to become less important. In doing so, vGNM is able to resolve the apparent discrepancy in experimental B-factors among structures of the same protein but with different crystal packing conditions, which GNM cannot explain. With a small number of parameters, vGNM is able to reproduce experimental B-factors for a large set of proteins with significantly better correlations (having a mean value of 0.81 as compared to 0.59 by GNM). The results of applying vGNM also show that the rigid body motions account for nearly 60% of the total fluctuations, in good agreement with previous findings.     

The effects of depowered airbags on skin injuries in frontal automobile crashes

The purpose of this study was to determine the effects of depowered frontal airbags on the incidence of skin injuries. The National Automotive Sampling System database files from 1993 to 2000 were examined in a study including 2,246,524 occupants exposed to airbag deployment in the United States. There was no significant difference between full-powered and depowered airbags, with 60.2 percent of those exposed to a full-powered deployment sustaining a skin injury versus 59.5 percent of occupants exposed to a depowered airbag (p = 0.19). Whether occupants were exposed to a full-powered airbag (1,936,485 occupants) or a depowered airbay (310,039 occupants), the majority of skin injuries were to the upper extremity and the face. Regardless of airbag power, the overwhelming majority of the skin injuries were minor (99.8 percent). There was not a significantly greater risk of injury from any source for occupants exposed to a depowered airbag or a full-powered airbag (p = 0.87). The data suggest that the implementation of depowered airbags did not affect the number, seriousness, location, or source of skin injuries.     

Rigid-cluster models of conformational transitions in macromolecular machines and assemblies

We present a rigid-body-based technique (called rigid-cluster elastic network interpolation) to generate feasible transition pathways between two distinct conformations of a macromolecular assembly. Many biological molecules and assemblies consist of domains which act more or less as rigid bodies during large conformational changes. These collective motions are thought to be strongly related with the functions of a system. This fact encourages us to simply model a macromolecule or assembly as a set of rigid bodies which are interconnected with distance constraints. In previous articles, we developed coarse-grained elastic network interpolation (ENI) in which, for example, only Calpha atoms are selected as representatives in each residue of a protein. We interpolate distance differences of two conformations in ENI by using a simple quadratic cost function, and the feasible conformations are generated without steric conflicts. Rigid-cluster interpolation is an extension of the ENI method with rigid-clusters replacing point masses. Now the intermediate conformations in an anharmonic pathway can be determined by the translational and rotational displacements of large clusters in such a way that distance constraints are observed. We present the derivation of the rigid-cluster model and apply it to a variety of macromolecular assemblies. Rigid-cluster ENI is then modified for a hybrid model represented by a mixture of rigid clusters and point masses. Simulation results show that both rigid-cluster and hybrid ENI methods generate sterically feasible pathways of large systems in a very short time. For example, the HK97 virus capsid is an icosahedral symmetric assembly composed of 60 identical asymmetric units. Its original Hessian matrix size for a Calpha coarse-grained model is >(300,000)(2). However, it reduces to (84)(2) when we apply the rigid-cluster model with icosahedral symmetry constraints. The computational cost of the interpolation no longer scales heavily with the size of structures; instead, it depends strongly on the minimal number of rigid clusters into which the system can be decomposed.     

Comparison of tRNA motions in the free and ribosomal bound structures

A general method is presented that allows the separation of the rigid body motions from the nonrigid body motions of structural subunits when bound in a complex. The application presented considers the motions of the tRNAs: free, bound to the ribosome and to a synthase. We observe that both the rigid body and nonrigid body motions of the structural subunits are highly controlled by the large ribosomal assembly and are important for the functional motions of the assembly. For the intact ribosome, its major parts, the 30S and the 50S subunits, are found to have counterrotational motions in the first few slowest modes, which are consistent with the experimentally observed ratchet motion. The tRNAs are found to have on average approximately 72-75% rigid body motions and principally translational motions within the first 100 slow modes of the complex. Although the three tRNAs exhibit different apparent total motions, after the rigid body motions are removed, the remaining internal motions of all three tRNAs are essentially the same. The direction of the translational motions of the tRNAs are in the same direction as the requisite translocation step, especially in the first slowest mode. Surprisingly the small intrinsically flexible mRNA has all of its internal motions completely inhibited and shows mainly a rigid-body translation in the slow modes of the ribosome complex. On the other hand, the required nonrigid body motions of the tRNA during translocation reveal that the anticodon-stem-loop, as well as the acceptor arm, of the tRNA enjoy a large mobility but act as rigid structural units. In summary, the ribosome exerts its control by enforcing rigidity in the functional parts of the tRNAs as well as in the mRNA.     

Molecular mechanism of domain swapping in proteins: an analysis of slower motions

Domain swapping is a structural phenomenon that plays an important role in the mechanism of oligomerization of some proteins. The monomer units in the oligomeric structure become entangled with each other. Here we investigate the mechanism of domain swapping in diphtheria toxin and the structural criteria required for it to occur by analyzing the slower modes of motion with elastic network models, Gaussian network model and anisotropic network model. We take diphtheria toxin as a representative of this class of domain-swapped proteins and show that the domain, which is being swapped in the dimeric state, rotates and twists, in going from the "open" to the "closed" state, about a hinge axis that passes through the middle of the loop extending between two domains. A combination of the intra- and intermolecular contacts of the dimer is almost equivalent to that of the monomer, which shows that the relative orientations of the residues in both forms are almost identical. This is also reflected in the calculated B-factors when compared with the experimentally determined B-factors in x-ray crystal structures. The slowest modes of both the monomer and dimer show a common hinge centered on residue 387. The differences in distances between the monomer and the dimer also shows the hinge at nearly the same location (residue 381). Finally, the first three dominant modes of anisotropic network model together shows a twisting motion about the hinge centered on residue 387. We further identify the location of hinges for a set of another 12 domain swapped proteins and give the quantitative measures of the motions of the swapped domains toward their "closed" state, i.e., the overlap and correlation between vectors.